Fulde-Ferrell-Larkin-Ovchinnikov state in layered superconductors

The phase diagram of a layered superconductor in a large parallel magnetic field is calculated. This includes a calculation of the lower critical field beyond which the superconductor is in the FFLO-state and possesses a spatially modulated order parameter and spin polarization. The order parameter, spin polarization, free-energy density, and phase boundaries of this unconventional superconducting phase are evaluated numerically in the complete B–T plane. The analysis suggests that the transition at the lower critical field is of second order, and not of first order, as previously assumed. The order parameter of the FFLO-state merges continuously into the uniform superconducting state.     

Fermionic entropy of the vortex state in d-wave superconductors

In d-wave superconductors the electronic entropy associated with an isolated vortex diverges logarithmically with the size of the system even at low temperatures. In the vortex array the entropy per vortex per layer, S _V , is much larger than k _B and depends on the distribution of the velocity field v _s around the vortex. If there is a first-order transition upon a change of the velocity distribution, then there will be a big entropy jump ΔS _V ∼k _B at the transition. This entropy jump comes from the electronic degrees of freedom on the vortex background, which is modified by the vortex transition. This can explain the big jump in the entropy observed in the so-called vortex-melting transition [A. Junod, M. Roulin, J-Y. Genoud et al., Physica C, to be published], in which the vortex array and thus the velocity field are redistributed. The possibility of the Berezinskii-Kosterlitz-Thouless transition in the 3-dimensional d-wave superconductor due to the fermionic bound states in the vortex background is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 465–469 (25 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Index theoretic characterization of d-wave superconductors in the vortex state

We study analytically the low energy spectrum of a lattice d-wave superconductor in the vortex lattice state. For an inversion symmetric hc/2e vortex lattice and in the presence of particle-hole symmetry we prove an index theorem that imposes a lower bound on the number of zero-energy modes. Generic cases are constructed in which this bound exceeds the number of zero modes of an equivalent lattice of hc/e vortices, despite the identical point group symmetries. The quasiparticle spectrum around the zero modes is doubly degenerate and exhibits a Dirac-like dispersion, with velocities that become universal functions of Delta(0)/t in the limit of low magnetic field. For weak particle-hole symmetry breaking, the gapped state can be characterized by a topological quantum number, related to spin-Hall conductivity, which generally differs in the cases of the hc/2e and hc/e vortex lattices.     

Weak-field thermal hall conductivity in the mixed state of d-wave superconductors

Thermal transport in the mixed state of a d-wave superconductor is considered within the weak-field regime. We express the thermal conductivity, kappa(xx), and the thermal Hall conductivity, kappa(xy), in terms of the cross section for quasiparticle scattering from a single vortex. Solving for the cross section (neglecting the Berry phase contribution and the anisotropy of the gap nodes), we obtain kappa(xx)(H,T) and kappa(xy)(H,T) in surprisingly good agreement with the qualitative features of the experimental results for YBa2Cu3O6.99. In particular, we show that the simple, yet previously unexpected, weak-field behavior, kappa(xy)(H,T) approximately T squareroot [H], is that of thermally excited nodal quasiparticles, scattering primarily from impurities, with a small skew component provided by vortex scattering.     

Pairing state of high-T c superconductors: Comments on the Josephson effect experiments in the context of the s- vs. d-wave debate

Il Nuovo Cimento D - A variety of experimental investigations has been developed in the last years toward the identification of the symmetry of the order parameter in high-T c superconductors. A...     

Novel route to a finite center-of-mass momentum pairing state for superconductors: A current-driven Fulde-Ferrell-Larkin-Ovchinnikov state

The previously studied Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is stabilized by a magnetic field via the Zeeman coupling in spin-singlet superconductors. Here we suggest a novel route to achieve nonzero center-of-mass momentum pairing states in superconductors with Fermi surface nesting. We investigate two-dimensional superconductors under a uniform external current, proportional to a finite pair momentum of q(e). We find that an FFLO state with a spontaneous pair momentum of q(s) is stabilized above a certain critical current that depends on the direction of the external current. A finite q(s) arises in order to make the total pair-momentum of q(t)(=q(s) + q(e)) perpendicular to the nesting vector, which is independent of spin states of Cooper pairs. We also discuss experimental signatures of the FFLO state.     

Effects of a collective spin resonance mode on the scanning tunneling microscopy spectra of d-wave superconductors

A high-energy spin resonance mode is known to exist in many high-temperature superconductors. Motivated by recent scanning tunneling microscopy experiments in superconducting Bi(2)Sr(2)CaCu(2)O(8+delta), we study the effects of this resonance mode on the local density of states (LDOS). The coupling between the electrons in a d-wave superconductor and the resonance mode produces high-energy peaks in the LDOS, which displays a two-unit-cell periodic modulation around a nonmagnetic impurity. This suggests a new means to not only detect the dynamical spin collective mode but also study its coupling to electronic excitations.     

Spatial line nodes and fractional vortex pairs in the Fulde-Ferrell-Larkin-Ovchinnikov vortex state of spin-singlet superconductors

A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in spin-singlet superconductors. Here we argue that there is a nontrivial solution for the FFLO vortex phase that exists near the upper critical field in which the wave function has only spatial line nodes that form intricate and unusual three-dimensional structures. These structures include a crisscrossing lattice of two sets of nonparallel line nodes. We show that these solutions arise from the decay of conventional Abrikosov vortices into pairs of fractional vortices. We propose that neutron scattering studies can observe these fractional vortex pairs through the observation of a lattice of 1/2 flux quanta vortices. We also consider related phases in noncentrosymmetric superconductors.     

Discrete-lattice model approach to the tunneling between d-wave superconductors: Interference of tunnel bonds

The Josephson current between d-wave superconductors is investigated in the framework of the tight-binding lattice model. The junction is modeled by a small number of connecting bonds. It is found that the Josephson current through one bond vanishes when at least one of the superconductors has the (110) interface-to-crystal orientation. Interference between the nearest bonds appears to be very important. In particular, it is the interference term that leads to the nonzero Josephson current for the (110) orientation. Also, interference of two connecting bonds manifests itself in nonmonotonic behavior of the critical Josephson current in a dependence on the distance between the bonds. The text was submitted by the author in English.     

铁基超导体的扫描隧道显微镜研究进展

铁基高温超导体自2008年发现以来,对其超导电性的研究一直是一个热门的课题.扫描隧道显微镜能够在原子尺度进行表面形貌和隧道谱测量,从微观角度研究电子态密度的信息,是研究超导的重要谱学手段.近年来,在铁基超导电性方面,扫描隧道显微镜实验已经积累了一些有价值的结果,本文进行了总结介绍.铁基超导体是多带多超导能隙的超导体,不同材料的费米面结构有很大的变化.扫描隧道显微镜证明,同时有电子和空穴费米面最佳掺杂的铁基样品超导能隙结构是无节点并带有能隙符号变化的s^±波.而进一步的实验发现在没有空穴费米面的FeSe基超导体中也存在能隙符号的相反,对统一铁基超导体的配对对称性提供了重要实验证据.此外,扫描隧道显微镜在研究铁基超导体的电子向列相、浅能带特性、可能的拓扑特性方面,提供了重要的实验数据.本文对上述相关内容进行了总结,并做了相应分析和讨论.     

Topological structure of a vortex in the Fulde-Ferrell-Larkin-Ovchinnikov state

We find theoretically that the vortex core in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is quite different from the ordinary core for a simple topological reason. The intersection point of a vortex and nodal plane of the FFLO state empties the excess spins. This leads to observable consequences in the spatial structure of the spontaneous magnetization. We analyze this topological structure based on the low lying excitation spectrum by solving a microscopic Bogoliubov-de Gennes equation to clarify its physical origin.     

Theory of tunneling spectroscopy in the Larkin-Ovchinnikov state

We present a theory of tunneling spectroscopy for normal metal/Larkin-Ovchinnikov state junctions in which the spatial periodic modulation in the pair potential amplitude is taken into account. The tunneling spectra show the characteristic line shapes reflecting the minigap structures under the periodic pair potentials depending on the boundary condition of the pair potentials at the junction interface. These features are qualitatively different from the tunneling spectra of the Fulde-Ferrell state. We propose an experimental setup which identifies the superconducting state of CeCoIn5.     

On the problem of zero-bias anomalies in the tunneling spectroscopy of superconductors

Taking into account nonmagnetic energy-loss processes in the barrier as a model for zero-bias anomalies, we derive an expression for the derivative of the tunneling current with respect to the applied voltage as a function of the superconducting density of states in a superconductor-normal metal junction. It is assumed that boson-like excitations are created in the barrier region. The investigations show, that the results of elastic tunneling calculations have to be corrected by a term proportional to an integral over the superconducting density of states.     

Vortex dynamics and the Fulde-Ferrell-Larkin-Ovchinnikov state in a magnetic-field-induced organic superconductor

Under special conditions, a superconducting state where the order parameter oscillates in real space, the so-called FFLO state, is theoretically predicted to exist near the upper critical field, as first proposed by Fulde and Ferrell, and Larkin and Ovchinnikov. We report systematic measurements of the interlayer resistance in high magnetic fields to 45 T in the two-dimensional magnetic-field-induced organic superconductor lambda-(BETS)2FeCl4, where BETS is bis(ethylenedithio)tetraselenafulvalene. The resistance is found to show characteristic dip structures in the superconducting state. The results are consistent with pinning interactions between the vortices penetrating the insulating layers and the order parameter of the FFLO state. This gives strong evidence for an oscillating order parameter in real space.     

Thermal conductivity and competing orders in d-wave superconductors

We derive the expression for the thermal conductivity in the low-temperature limit in d-wave superconductors, taking into account the presence of competing orders such as spin-density wave, is-pairing, etc. The expression is used for analyzing recent experimental data in . Our analysis strongly suggests that competing orders can be responsible for anomalies in behavior of thermal conductivity observed in those experiments.Received: 9 December 2003, Published online: 2 April 2004PACS: 74.25.Fy Transport properties (electric and thermal conductivity, thermoelectric effects, etc.) - 74.72.Dn La-based cuprates - 74.72.-h Cuprate superconductors (high-Tc and insulating parent compounds)V.P. Gusynin: On leave from Bogolyubov Institute for Theoretical Physics, 03143 Kiev, UkraineV.A. Miransky: On leave from Bogolyubov Institute for Theoretical Physics, 03143 Kiev, Ukraine